Conference Agenda

Rayleigh-Benard convection (RBC) at high Rayleigh (Ra) numbers represents one of the most important model systems to study turbulent convection [1]. Experiments reaching very high Ra, approaching values relevant for convective systems in Nature, like the atmospheric convection, have been performed using various working uids, prominently with cryogenic helium 4He [2] and sulphur hexafluoride SF6 [3]. The goal of attaining high Ra often comes at the cost of breaking the Oberbeck-Boussinesq (OB) conditions at the phase boundaries or near the critical points of the working fluids. In particular, the recent analysis [4] of RBC experiments performed near the saturated vapor curves (SVC) in 4He and SF6 indicates that the heat transport measurements of the Nusselt number Nu(Ra), which apparently show the transition of RBC to the ultimate Kraichnan regime, are significantly affected by non-OB (NOB) effects, thus keeping the question of experimental observation of the ultimate regime open. The present study investigates the NOB effects which arise due to the temperature dependence of material properties in cryogenic helium experiments of turbulent RBC. The material properties such as specific heat at constant pressure, dynamic viscosity, thermal conductivity, the isobaric expansivity, and the mass density are expanded into power series with respect to temperature up to the quadratic order with coeffcients obtained from the software package HEPAK. A subsequent nonlinear regression that uses deep convolutional networks delivers a dependence of the strength of NOB effects in the pressure{temperature parameter plane. Strength of the NOB effects is evaluated via the deviation of the mean temperature profile $\xi_{NOB} \equiv T_m-T_c$ from the top/bottom-symmetric OB case $\xi_{NOB} = 0$. Training data for the regression task are obtained from 236 individual long-term laboratory measurements at different Rayleigh numbers which span 8 orders of magnitude. The work has been supported by the Czech Science Foundation project No. 21-06012J.

References

[1] G. Ahlers, S. Grossmann and D. Lohse, Rev. Mod. Phys., 81, 503, 2009.

[2] L. Skrbek and P. Urban, Journal of Fluid Mechanics, 785, 270, 2015.

[3] X. He, D. Funfschilling, H. Nobach, E. Bodenschatz and G. Ahlers, Phys. Rev. Letters, 108, 024502, 2012.

[4] P. Urban, P. Hanzelka, T. Kralk, M. Macek, V. Musilova and L. Skrbek, Phys. Rev. E, 99, 011101(R), 2019.

[5] D. D. Gray and A. Giorgini, Int. J. Heat Mass Transfer, 19, 545, 1976.

Stratified turbulent flows abound in environmental and industrial settings. Examples are atmospheric boundary layer flows, the transport of nutrients and organisms and the mixing of heat and salinity in the oceans, fluid flow in heat exchangers, and the transport of reactants and products in chemical reactions. These examples and many others consider stratified wall-bounded turbulence, in which the creation of turbulence by mechanical processes contends with its dissipation due to buoyancy effects. The buoyancy effects alter the structure of the flow, and consequently the dynamics of mass, heat, and momentum transport. As density fluctuations become more severe, the Oberbeck-Boussinesq approximation becomes inaccurate and the resulting dynamics are not correctly predicted. In the current work, we developed and validated a numerical solver for direct numerical simulations (DNS) of turbulent flows featuring strong property variations. More precisely, we solve the Navier-Stokes equations in the limit of vanishing Mach number (so-called low-Mach number limit), with the fluid density given by the ideal gas law, and the dynamic viscosity and thermal conductivity given by Sutherland's law.

Our numerical solver was then used to study stably-stratified turbulent channel flow under non-Oberbeck-Boussinesq conditions. The simulations will be carried out at friction Reynolds number of 395, Prandtl number of 0.71, and shear Richardson number in the O(10), where the friction Reynolds, Prandtl, and friction Richardson numbers are governing parameters defined based on the prescribed pressure drop and properties of the fluid at the reference temperature. Stratification is achieved by imposing constant temperature boundary conditions, with a high upper-to-lower wall temperature ratio (larger than 2), resulting in strong density variations in the flow. We will vary the temperature ratios and adjust gravity to maintain a similar Richardson number between cases, thereby isolating the effects of strong property variations in the flow dynamics. In the presentation, we will analyze the dynamics of heat and momentum transport under strong stratification for these conditions, also in light of DNS data of the same system under the Oberbeck-Boussinesq regime.

Transport phenomena in high Reynolds number wall-bounded stratified flows are dominated by the interplay between the turbulence structures generated at the wall and the buoyancy-induced large scale waves populating the channel core. In this study, we want to investigate the flow physics of wall-bounded stratified turbulence at relatively high shear Reynolds number Ret and for mild to moderate stratification level (quantified here by the shear Richardson number varying in the range 0<Rit<300). By increasing stratification, active turbulence is sustained only in the near-wall region, whereas intermittent turbulence, modulated by the presence of non-turbulent wavy structures (Internal Gravity Waves, IGW), is observed at the channel core. In such conditions, the wall-normal transport of momentum and heat is considerably reduced compared to the case of non-stratified turbulence. A careful characterization of the flow-field statistics shows that, despite temperature and wall-normal velocity fluctuations are very large at the channel center, the mean value of their product (buoyancy flux) vanishes for Rit>200. We show that this behavior is due to the presence of a pi/2 phase delay between the temperature and the wall-normal velocity signals: when wall-normal velocity fluctuations are large (in magnitude), temperature fluctuations are almost zero, and viceversa. This constitutes a blockage effect to the wall-normal exchange of energy. In addition, we show that the friction factor scales as a power of the Richardson number (-1/3), and we propose a new scaling for the Nusselt number (as a function of Reynolds and Richardson number). These scaling laws, which seem robust over the explored range of parameters, are expected to help the development of improved models and parametrizations of stratified flows at large Re.